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Rahul Shetty

Publications and source records attributed to Rahul Shetty.

At least 19 recordsLinked to original sources

Moving On, Even When You're Broken: Fail-Active Trajectory Generation via Diffusion Policies Conditioned on Embodiment and Task

Robot failure is detrimental and disruptive, often requiring human intervention to recover. Our vision is 'fail-active' operation, allowing robots to safely complete their tasks even when damaged. Focusing on 'actuation failures', we introduce DEFT, a diffusion-based trajectory generator conditioned on the robot's current embodiment and task constraints. DEFT generalizes across failure types, supports constrained and unconstrained motions, and enables task completion under arbitrary failure. We evaluate DEFT in both simulation and real-world scenarios using a 7-DoF robotic arm. DEFT outperforms its baselines over thousands of failure conditions, achieving a 99.5% success rate for unconstrained motions versus RRT's 42.4%, and 46.4% for constrained motions versus differential IK's 30.9%. Furthermore, DEFT demonstrates robust zero-shot generalization by maintaining performance on failure conditions unseen during training. Finally, we perform real-world evaluations on two multi-step tasks, drawer manipulation and whiteboard erasing. These experiments demonstrate DEFT succeeding on tasks where classical methods fail. Our results show that DEFT achieves fail-active manipulation across arbitrary failure configurations and real-world deployments.

cs.RO

Using CO line ratios to trace the physical properties of molecular clouds

The carbon monoxide (CO) rotational transition lines are the most common tracers of molecular gas within giant molecular clouds (MCs). We study the ratio ($R_{2-1/1-0}$) between CO's first two emission lines and examine what information it provides about the physical properties of the cloud. To study $R_{2-1/1-0}$ we perform smooth particle hydrodynamic simulations with time dependent chemistry (using GADGET-2), along with post-process radiative transfer calculations on an adaptive grid (using RADMC-3D) to create synthetic emission maps of a MC. $R_{2-1/1-0}$ has a bimodal distribution that is a consequence of the excitation properties of each line, given that $J=1$ reaches local thermal equilibrium (LTE) while $J=2$ is still sub-thermally excited in the considered clouds. The bimodality of $R_{2-1/1-0}$ serves as a tracer of the physical properties of different regions of the cloud and it helps constrain local temperatures, densities and opacities. Additionally this bimodal structure shows an important portion of the CO emission comes from diffuse regions of the cloud, suggesting that the commonly used conversion factor of $R_{2-1/1-0}\sim 0.7$ between both lines may need to be studied further.

astro-ph.GA

Simultaneously modelling far-infrared dust emission and its relation to CO emission in star forming galaxies

We present a method to simultaneously model the dust far-infrared spectral energy distribution (SED) and the total infrared $-$ carbon monoxide (CO) integrated intensity $(S_{\rm IR}-I_{\rm CO})$ relationship. The modelling employs a hierarchical Bayesian (HB) technique to estimate the dust surface density, temperature ($T_{\rm eff}$), and spectral index at each pixel from the observed far-infrared (FIR) maps. Additionally, given the corresponding CO map, the method simultaneously estimates the slope and intercept between the FIR and CO intensities, which are global properties of the observed source. The model accounts for correlated and uncorrelated uncertainties, such as those present in Herschel observations. Using synthetic datasets, we demonstrate the accuracy of the HB method, and contrast the results with common non-hierarchical fitting methods. As an initial application, we model the dust and gas on 100 pc scales in the Magellanic Clouds from Herschel FIR and NANTEN CO observations. The slopes of the $\log S_{\rm IR}-\log I_{\rm CO}$ relationship are similar in both galaxies, falling in the range 1.1$-$1.7. However, in the SMC the intercept is nearly 3 times higher, which can be explained by its lower metallicity than the LMC, resulting in a larger $S_{\rm IR}$ per unit $I_{\rm CO}$. The HB modelling evidences an increase in $T_{\rm eff}$ in regions with the highest $I_{\rm CO}$ in the LMC. This may be due to enhanced dust heating in the densest molecular regions from young stars. Such simultaneous dust and gas modelling may reveal variations in the properties of the ISM and its association with other galactic characteristics, such as star formation rates and/or metallicities.

astro-ph.GA

Distribution and mass of diffuse and dense CO gas in the Milky Way

Emission from carbon monoxide (CO) is ubiquitously used as a tracer of dense star forming molecular clouds. There is, however, growing evidence that a significant fraction of CO emission originates from diffuse molecular gas. Quantifying the contribution of diffuse CO-emitting gas is vital for understanding the relation between molecular gas and star formation. We examine the Galactic distribution of two CO-emitting gas components, a high column density component detected in 13CO and 12CO, and a low column density component detected in 12CO, but not in 13CO. The "diffuse" and "dense" components are identified using a combination of smoothing, masking, and erosion/dilation procedures, making use of three large-scale 12CO and 13CO surveys of the Inner and Outer Milky Way. The diffuse component, which globally represents 25 (1.5x1e8 Mo) of the total molecular gas mass (6.5x1e8 Mo), is more extended perpendicular to the Galactic plane. The fraction of diffuse gas increases from 15% at a galactocentric radius of 3 kpc to 50% at 15 kpc, and increases with decreasing surface density. In the Inner Galaxy, a yet denser component traced by CS emission represents 14% of the total molecular gas mass traced by 12CO emission. Only 14% of the molecular gas mass traced by 12CO emission is identified as part of molecular clouds in 12CO surveys by cloud identification algorithms. This study indicates that CO emission not only traces star forming clouds, but also a significant diffuse molecular ISM component.

astro-ph.GA

Mach number study of supersonic turbulence: The properties of the density field

We model driven, compressible, isothermal, turbulence with Mach numbers ranging from the subsonic ($\mathcal{M} \approx 0.65$) to the highly supersonic regime ($\mathcal{M}\approx 16 $). The forcing scheme consists both solenoidal (transverse) and compressive (longitudinal) modes in equal parts. We find a relation $σ_{s}^2 = \mathrm{b}\log{(1+\mathrm{b}^2\mathcal{M}^2)}$ between the Mach number and the standard deviation of the logarithmic density with $\mathrm{b} = 0.457 \pm 0.007$. The density spectra follow $\mathcal{D}(k,\,\mathcal{M}) \propto k^{ζ(\mathcal{M})}$ with scaling exponents depending on the Mach number. We find $ζ(\mathcal{M}) = α\mathcal{M}^β$ with a coefficient $α$ that varies slightly with resolution, whereas $β$ changes systematically. We extrapolate to the limit of infinite resolution and find $α= -1.91 \pm 0.01,\, β=-0.30\pm 0.03$. The dependence of the scaling exponent on the Mach number implies a fractal dimension $D=2+0.96 \mathcal{M}^{-0.30}$. We determine how the scaling parameters depend on the wavenumber and find that the density spectra are slightly curved. This curvature gets more pronounced with increasing Mach number. We propose a physically motivated fitting formula $\mathcal{D}(k) = \mathcal{D}_0 k^{ζk^η}$ by using simple scaling arguments. The fit reproduces the spectral behaviour down to scales $k\approx 80$. The density spectrum follows a single power-law $η= -0.005 \pm 0.01$ in the low Mach number regime and the strongest curvature $η= -0.04 \pm 0.02$ for the highest Mach number. These values of $η$ represent a lower limit, as the curvature increases with resolution.

astro-ph.SR

Tracing the general structure of Galactic molecular clouds using Planck data: I. The Perseus region as a test case

We present an analysis of probability distribution functions (pdfs) of column density in different zones of the star-forming region Perseus and its diffuse environment based on the map of dust opacity at 353 GHz available from the Planck archive. The pdf shape can be fitted by a combination of a lognormal function and an extended power-law tail at high densities, in zones centred at the molecular cloud Perseus. A linear combination of several lognormals fits very well the pdf in rings surrounding the cloud or in zones of its diffuse neighbourhood. The slope of the mean density scaling law $\langleρ\rangle_L \propto L^α$ is steep ($α=-1.93$) in the former case and rather shallow ($α=-0.77\pm0.11$) in the rings delineated around the cloud. We interpret these findings as signatures of two distinct physical regimes: i) a gravoturbulent one which is characterized by nearly linear scaling of mass and practical lack of velocity scaling; and ii) a predominantly turbulent one which is best described by steep velocity scaling and by invariant for compressible turbulence $\langleρ\rangle_L u_L^3/L$, describing a scale-independent flux of the kinetic energy per unit volume through turbulent cascade. The gravoturbulent spatial domain can be identified with the molecular cloud Perseus while a relatively sharp transition to predominantly turbulent regime occurs in its vicinity.

astro-ph.GA

Hierarchical Bayesian analysis of the velocity power spectrum in supersonic turbulence

Turbulence is a dominant feature operating in gaseous flows across nearly all scales in astrophysical environments. Accordingly, accurately estimating the statistical properties of such flows is necessary for developing a comprehensive understanding of turbulence. We develop and employ a hierarchical Bayesian fitting method to estimate the parameters describing the scaling relationships of the velocity power spectra of supersonic turbulence. We demonstrate the accuracy and other advantages of this technique compared with ordinary linear regression methods. Using synthetic power spectra, we show that the Bayesian method provides accurate parameter and error estimates. Commonly used normal linear regression methods can provide estimates that fail to recover the underlying slopes, up to 70% of the instances, even when considering the 2std.dev. uncertainties. Additionally, we apply the Bayesian methods to analyse the statistical properties of compressible turbulence in 3D numerical simulations. We model driven, isothermal, turbulence with rms Mach numbers in the highly supersonic regime M~15. We study the influence of purely solenoidal (divergence-free) and purely compressive (curl-free) forcing on the scaling exponent of the power spectrum. In simulations with solenoidal forcing and 1024^3 resolution, our results indicate that there is no extended inertial range with a constant scaling exponent. The bottleneck effect results in a curved power spectrum at all wave numbers and is more pronounced in the transversal modes compared with the longitudinal modes. Therefore, this effect is stronger in stationary turbulent flows driven by solenoidal forcing compared to the compressive one. The longitudinal spectrum driven with compressive forcing is the only spectrum with constant scaling exponent z=-1.94 +- 0.01, corresponding to slightly shallower slopes than the Burger's prediction.

astro-ph.SR

Centroid Velocity Statistics of Molecular Clouds

We compute structure functions and Fourier spectra of 2D centroid velocity (CV) maps in order to study the gas dynamics of typical molecular clouds (MCs) in numerical simulations. We account for a simplified treatment of time-dependent chemistry and the non-isothermal nature of the gas and use a 3D radiative transfer tool to model the CO line emission in a post-processing step. We perform simulations using three different initial mean number densities of n_0 = 30, 100 and 300 cm^{-3} to span a range of typical values for dense gas clouds in the solar neighbourhood. We compute slopes of the centroid velocity increment structure functions (CVISF) and of Fourier spectra for different chemical components: the total density, H2 number density, 12CO number density as well as the integrated intensity of 12CO (J=1-0) and 13CO (J=1-0). We show that optical depth effects can significantly affect the slopes derived for the CVISF, which also leads to different scaling properties for the Fourier spectra. The slopes of CVISF and Fourier spectra for H2 are significantly steeper than those for the different CO tracers, independent of the density and the numerical resolution. This is due to the larger space-filling factor of H2 as it is better able to self-shield in diffuse regions, leading to a larger fractal co-dimension compared to CO.

astro-ph.SR

Line Profiles of Cores within Clusters. III. What is the most reliable tracer of core collapse in dense clusters?

Recent observational and theoretical investigations have emphasised the importance of filamentary networks within molecular clouds as sites of star formation. Since such environments are more complex than those of isolated cores, it is essential to understand how the observed line profiles from collapsing cores with non-spherical geometry are affected by filaments. In this study, we investigate line profile asymmetries by performing radiative transfer calculations on hydrodynamic models of three collapsing cores that are embedded in filaments. We compare the results to those that are expected for isolated cores. We model the five lowest rotational transition line (J = 1-0, 2-1, 3-2, 4-3, and 5-4) of both optically thick (HCN, HCO$^+$) as well as optically thin (N$_2$H$^+$, H$^{13}$CO$^+$) molecules using constant abundance laws. We find that less than 50% of simulated (1-0) transition lines show blue infall asymmetries due to obscuration by the surrounding filament. However, the fraction of collapsing cores that have a blue asymmetric emission line profile rises to 90% when observed in the (4-3) transition. Since the densest gas towards the collapsing core can excite higher rotational states, upper level transitions are more likely to produce blue asymmetric emission profiles. We conclude that even in irregular, embedded cores one can trace infalling gas motions with blue asymmetric line profiles of optically thick lines by observing higher transitions. The best tracer of collapse motions of our sample is the (4-3) transition of HCN, but the (3-2) and (5-4) transitions of both HCN and HCO$^+$ are also good tracers.

astro-ph.SR

Interpreting the sub-linear Kennicutt-Schmidt relationship: The case for diffuse molecular gas

Recent statistical analysis of two extragalactic observational surveys strongly indicate a sublinear Kennicutt-Schmidt (KS) relationship between the star formation rate (Sigsfr) and molecular gas surface density (Sigmol). Here, we consider the consequences of these results in the context of common assumptions, as well as observational support for a linear relationship between Sigsfr and the surface density of dense gas. If the CO traced gas depletion time (tau_mol) is constant, and if CO only traces star forming giant molecular clouds (GMCs), then the physical properties of each GMC must vary, such as the volume densities or star formation rates. Another possibility is that the conversion between CO luminosity and Sigmol, the XCO factor, differs from cloud-to-cloud. A more straightforward explanation is that CO permeates the hierarchical ISM, including the filaments and lower density regions within which GMCs are embedded. A number of independent observational results support this description, with the diffuse gas comprising at least 30% of the total molecular content. The CO bright diffuse gas can explain the sublinear KS relationship, and consequently leads to an increasing tau_mol with Sigmol. If Sigsfr linearly correlates with the dense gas surface density, a sublinear KS relationship indicates that the fraction of diffuse gas fdiff grows with Sigmol. In galaxies where Sigmol falls towards the outer disk, this description suggests that fdiff also decreases radially.

astro-ph.GA

Principal Component Analysis of Molecular Clouds: Can CO reveal the dynamics?

We use Principal Component Analysis (PCA) to study the gas dynamics in numerical simulations of typical MCs. Our simulations account for the non-isothermal nature of the gas and include a simplified treatment of the time-dependent gas chemistry. We model the CO line emission in a post-processing step using a 3D radiative transfer code. We consider mean number densities n_0 = 30, 100, 300 cm^{-3} that span the range of values typical for MCs in the solar neighbourhood and investigate the slope α_{PCA} of the pseudo structure function computed by PCA for several components: the total density, H2 density, 12CO density, 12CO J = 1 -> 0 intensity and 13CO J = 1 -> 0 intensity. We estimate power-law indices α_{PCA} for different chemical species that range from 0.5 to 0.9, in good agreement with observations, and demonstrate that optical depth effects can influence the PCA. We show that when the PCA succeeds, the combination of chemical inhomogeneity and radiative transfer effects can influence the observed PCA slopes by as much as ~ +/- 0.1. The method can fail if the CO distribution is very intermittent, e.g. in low-density clouds where CO is confined to small fragments.

astro-ph.SR

The CO-to-H2 Conversion Factor across the Perseus Molecular Cloud

We derive the CO-to-H2 conversion factor, X_CO = N(H2)/I_CO, across the Perseus molecular cloud on sub-parsec scales by combining the dust-based N(H2) data with the I_CO data from the COMPLETE Survey. We estimate an average X_CO ~ 3 x 10^19 cm^-2 K^-1 km^-1 s and find a factor of ~3 variations in X_CO between the five sub-regions in Perseus. Within the individual regions, X_CO varies by a factor of ~100, suggesting that X_CO strongly depends on local conditions in the interstellar medium. We find that X_CO sharply decreases at Av < 3 mag but gradually increases at Av > 3 mag, with the transition occurring at Av where I_CO becomes optically thick. We compare the N(HI), N(H2), I_CO, and X_CO distributions with two models of the formation of molecular gas, a one-dimensional photodissociation region (PDR) model and a three-dimensional magnetohydrodynamic (MHD) model tracking both the dynamical and chemical evolution of gas. The PDR model based on the steady state and equilibrium chemistry reproduces our data very well but requires a diffuse halo to match the observed N(HI) and I_CO distributions. The MHD model generally matches our data well, suggesting that time-dependent effects on H2 and CO formation are insignificant for an evolved molecular cloud like Perseus. However, we find interesting discrepancies, including a broader range of N(HI), likely underestimated I_CO, and a large scatter of I_CO at small Av. These discrepancies likely result from strong compressions/rarefactions and density fluctuations in the MHD model.

astro-ph.GA

Indications of a sub-linear and non-universal Kennicutt-Schmidt relationship

We estimate the parameters of the Kennicutt-Schmidt (KS) relationship, linking the star formation rate (Sigma_SFR) to the molecular gas surface density (Sigma_mol), in the STING sample of nearby disk galaxies using a hierarchical Bayesian method. This method rigorously treats measurement uncertainties, and provides accurate parameter estimates for both individual galaxies and the entire population. Assuming standard conversion factors to estimate Sigma_SFR and Sigma_mol from the observations, we find that the KS parameters vary between galaxies, indicating that no universal relationship holds for all galaxies. The KS slope of the whole population is 0.76, with the 2sigma range extending from 0.58 to 0.94. These results imply that the molecular gas depletion time is not constant, but varies from galaxy to galaxy, and increases with the molecular gas surface density. Therefore, other galactic properties besides just Sigma_mol affect Sigma_SFR, such as the gas fraction or stellar mass. The non-universality of the KS relationship indicates that a comprehensive theory of star formation must take into account additional physical processes that may vary from galaxy to galaxy.

astro-ph.CO

Quantifying Observational Projection Effects Using Molecular Cloud Simulations

The physical properties of molecular clouds are often measured using spectral-line observations, which provide the only probes of the clouds' velocity structure. It is hard, though, to assess whether and to what extent intensity features in position-position-velocity (PPV) space correspond to "real" density structures in position-position-position (PPP) space. In this paper, we create synthetic molecular cloud spectral-line maps of simulated molecular clouds, and present a new technique for measuring the reality of individual PPV structures. Our procedure projects density structures identified in PPP space into corresponding intensity structures in PPV space and then measures the geometric overlap of the projected structures with structures identified from the synthetic observation. The fractional overlap between a PPP and PPV structure quantifies how well the synthetic observation recovers information about the 3D structure. Applying this machinery to a set of synthetic observations of CO isotopes, we measure how well spectral-line measurements recover mass, size, velocity dispersion, and virial parameter for a simulated star-forming region. By disabling various steps of our analysis, we investigate how much opacity, chemistry, and gravity affect measurements of physical properties extracted from PPV cubes. For the simulations used here, our results suggest that superposition induces a ~40% uncertainty in masses, sizes, and velocity dispersions derived from 13CO. The virial parameter is most affected by superposition, such that estimates of the virial parameter derived from PPV and PPP information typically disagree by a factor of ~2. This uncertainty makes it particularly difficult to judge whether gravitational or kinetic energy dominate a given region, since the majority of virial parameter measurements fall within a factor of 2 of the equipartition level alpha ~ 2.

astro-ph.GA

Relationship between molecular cloud structure and density PDFs

Volume and column density PDFs in molecular clouds are important diagnostics for understanding their general structure. We developed a novel approach to trace the cloud structure by varying the lower PDF cut-off and exploring a suggested mass-density relationship with a power-law index $x^\prime$. The correspondence of x' as a function of spatial scale to the slope of the high-density PDF tail is studied. To validate the proposed model, we use results from hydrodynamical simulations of a turbulent self-gravitating cloud and recent data on dust continuum emission from the Planck mission.

astro-ph.SR

Line Profiles of Cores within Clusters: II Signatures of Dynamical Collapse during High Mass Star Formation

Observations of atomic or molecular lines can provide important information about the physical state of star forming regions. In order to investigate the line profiles from dynamical collapsing massive star forming regions (MSFRs), we model the emission from hydrodynamic simulations of a collapsing cloud in the absence of outflows. By performing radiative transfer calculations, we compute the optically thick HCO+ and optically thin N2H+ line profiles from two collapsing regions at different epochs. Due to large-scale collapse, the MSFRs have large velocity gradients, reaching up to 20 km/s/pc across the central core. The optically thin lines typically contain multiple velocity components resulting from the superposition of numerous density peaks along the line-of-sight. The optically thick lines are only marginally shifted to the blue side of the optically thin line profiles, and frequently do not have a central depression in their profiles due to self-absorption. As the regions evolve the lines become brighter and the optically thick lines become broader. The lower order HCO+ (1-0) transitions are better indicators of collapse than the higher order (4-3) transitions. We also investigate how the beam sizes affect profile shapes. Smaller beams lead to brighter and narrower lines that are more skewed to the blue in HCO+ relative to the true core velocity, but show multiple components in N2H+. High resolution observations (e.g. with ALMA) can test these predictions and provide insights into the nature of MSFRs.

astro-ph.GA

On the temperature structure of the Galactic Centre cloud G0.253+0.016

We present a series of smoothed particle hydrodynamical models of G0.253+0.016 (also known as 'The Brick'), a very dense molecular cloud that lies close to the Galactic Centre. We explore how its gas and dust temperatures react as we vary the strength of both the interstellar radiation field (ISRF) and the cosmic ray ionisation rate (CRIR). As the physical extent of G0.253+0.016 along our line-of-sight is unknown, we consider two possibilities: one in which the longest axis is that measured in the plane of the sky (9.4 pc in length), and one in which it is along the line of sight, in which case we take it to be 17 pc. To recover the observed gas and dust temperatures, we find find that the ISRF must be around 1000 times the solar neighbourhood value, and the CRIR must be roughly 1E-14 /s, regardless of the geometries studied. For such high values of the CRIR, we find that cooling in the cloud's interior is dominated by neutral oxygen, in contrast to standard molecular clouds, which at the same densities are mainly cooled via CO. Our results suggest that the conditions near G0.253+0.016 are more extreme than those generally accepted for the inner 500 pc of the galaxy.

astro-ph.GA

Evidence for a non-universal Kennicutt-Schmidt relationship using hierarchical Bayesian linear regression

For investigating the relationship between the star formation rate and gas surface density, we develop a Bayesian linear regression method that rigorously treats measurement uncertainties and accounts for hierarchical data structure. The hierarchical method simultaneously estimates the intercept, slope, and scatter about the regression line of each individual subject and the population. Using synthetic datasets, we demonstrate that the method recovers the underlying parameters of both the individuals and the population, especially when compared to commonly employed ordinary least squares techniques, such as the bisector fit. We apply the hierarchical method to estimate the Kennicutt-Schmidt (KS) parameters of a sample of spiral galaxies compiled by Bigiel et al. (2008). We find significant variation in the KS parameters, indicating that no single relationship holds for all galaxies. This suggests that the relationship between molecular gas and star formation differs between galaxies, possibly due to the influence of other properties within a given galaxy, such as metallicity, molecular gas fraction, or stellar mass. In four galaxies the slope estimates are sub-linear (at the 95% level). We estimate the mean index of the KS relationship for the population to be 0.84, with 95% range [0.63, 1.0]. For the galaxies with sub-linear KS relationships, a possible interpretation is that CO emission is tracing some molecular gas that is not directly associated with star formation. Equivalently, a sub-linear KS relationship may be indicative of an increasing gas depletion time at higher surface densities, as traced by CO emission. The Bayesian method can account for all sources of uncertainties, including variations in the conversion of observed intensities to star formation rates and gas surface densities, and is therefore well suited for a thorough statistical analysis of the KS law.

astro-ph.CO